Vanessa set a school record for most points in a single basketball game when her team scored $48$ points. The six other players on her team averaged $3.5$ points each. How many points did Vanessa score to set her school record?
Answer: The six other players on the team averaged $3.5$ points each. The total of their points was $6\times 3.5=21.$ Vanessa scored the remainder of the points, or $48-21=\boxed{27}$ points.